2. Relations and Functions Mathematics Exercise - 2.3 class 11 Maths in English - CBSE Study
NCERT Solutions for Class 11 Mathematics are carefully prepared according to the latest CBSE syllabus and NCERT textbooks to help students understand every concept clearly. These solutions cover all important 2. Relations and Functions with detailed explanations and step-by-step answers for better exam preparation. Each Exercise 2.3 is explained in simple language so that students can easily grasp the fundamentals and improve their academic performance. The study material is designed to support daily homework, revision practice, and final exam preparation for Class 11 students. With accurate answers, concept clarity, and structured content, these NCERT solutions help learners build confidence and score higher marks in their examinations. Whether you are revising a specific topic or preparing an entire chapter, this resource provides reliable and syllabus-based guidance for complete success in Mathematics.
Class 11 English Medium Mathematics All Chapters:
2. Relations and Functions
3. Exercise 2.3
Exercise 2.3
Q1. Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
(i) {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}
(ii) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}
(iii) {(1,3), (1,5), (2,5)}.
Solution:
(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
Let be R = {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
There is no same component in the domain of given relation, so this relation is a function.
Here, domain = {2, 5, 8, 11, 14, 17} and range = {1}
Solution:
(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
Let be R = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
There are also unique domain components or order pair in the given relation, so this relation is a function.
Here, domain = {2, 4, 6, 8, 10, 12, 14} and range = {1, 2, 3, 4, 5, 6, 7}
Solution:
(iii) {(1, 3), (1, 5), (2, 5)}
Since the domain has the same first element i.e., 1 corresponds to two different images i.e.,
3 and 5, this relation is not a function.
Q2. Find the domain and range of the following real functions:
(i) f(x) = – |x|
Solution2:
Q3: A function f is defined by f(x) = 2x – 5
(i) f (0) (ii) f(7) (iii) f(-3)
Solution 3:
The given function is f(x) = 2x – 5
Therefore,
(i) f(0) = 2 × 0 – 5 = 0 – 5 = - 5
(ii) f(7) = 2 × 7 – 5 = 14 – 5 = - 9
(iii) f(-3) = 2 × -3 – 5 = -6 – 5 = - 11
Solution:
Solution:
(iii) f(x) = x is real number.
It is clear that the range of f is the set of all real number.
Therefore, range of f = R
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